Do mathematicians approach problems differently than physicists?

- James McDonald:
There is a (probably apocryphal) story about a group of scholars who wanted to figure out if von Neumann was more of a mathematician or a physicist, so they posed the following problem to him at a cocktail party: Two bicyclists start 20 miles apart and pedal towards each other, each at 10 mph. A bee starts on the handlebar of one bike and flies towards the other at 20 mph. Upon reaching that, it immediately turns around and flies back to the first bike, flitting back and forth until it is crushed when the bikes collide. How far does the bee fly before dying? If you’re a mathematician, you can set up an infinite series by noting that the bee flies 2/3 of the distance between the bikes on each leg. But you need to take into account the rate of the shrinking distance, etc., so it’s a little complicated to do in your head. A physicist would note that the bicyclists will pedal for one hour (10 miles at 10 mph), and the bee will thus travel 20 miles in that hour. Trivial solution. So they asked von Neumann and he instantly answered “20 miles”. Aha! They exclaimed — he’s a physicist. Tell everyone how you solved it. In bewilderment he looked at them and said “I summed the infinite series.” Update: Apparently the incident actually did happen (many thanks to Tamás Görbe for commenting with a video by Eugene Wigner describing the event), with Max Born posing the question to von Neumann about two bicyclists 40 miles apart, each pedaling at 20 mph, and a swallow flitting back and forth at 50 mph. When von Neumann instantly answered, Born said he was surprised because he was the first of his scientist friends to quickly solve it, after which von Neumann expressed surprise because it was such a simple geometric series to sum.

- Harold Anderson:
While in college in 1971 or 72, studying Industrial Design, I had an assignment to interview professors in most of the disciplines on campus to determine how they solved problems. I interview quite a few and all had their systems for solving problems. All used scientific methods until I got to the math department. The professor said he just thought about it. I asked more specifics. No, he just thought about it. I thought maybe I’d just met the one aberration on campus so interviewed at least two more math professors. I got the same from them all. All disciplines used scientific methods for solving problems except mathematicians.

- Martin Hogbin:
Yes. The difference is explained best by the various jokes about mathematicians and physicists, such as: An engineer, a physicist, and a mathematician were on a train heading north, and had just crossed the border into Scotland. The engineer looked out of the window and said "Look! Scottish sheep are black!" The physicist said, "No, no. Some Scottish sheep are black." The mathematician looked irritated. "There is at least one field, containing at least one sheep, of which at least one side is black." Which I got from here As a physicist I would just like to add that unless you are viewing from an infinite distance, in which case you would not be able to see the sheep at all, you can only see slightly less that one side of a sheep (with the normal asumptions).

- Yves Granger:
A chemist, a physicist and a mathematician are stranded on a desert island. They have a can of food they need to open. The chemist imagines a way with salted water turned into acid, slowly attacking the lid’s metal and finally letting them get the food. The physicist invents a device with a bent tree branch and a stone that could smash the tin open. The mathematician has been pacing around for some time and eventually says “assume a can opener.”.


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Video edited automatically by QRBot.

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